At the beginning of your upkeep, you may search your library for a Curse card that doesn't have the same name as a Curse attached to enchanted player, put it onto the battlefield attached to that player, then shuffle your library.

The Curse card you put onto the battlefield must have a different name than each other Curse enchanting the enchanted player when the triggered ability resolves. If multiple of these abilities trigger, the Curse card you put onto the battlefield when the first resolves may impact your choices for each subsequent one.